Ask most people what shape the Earth is and they will say a sphere. Ask someone with a slightly more technical background and they might say an "oblate spheroid" — a sphere flattened slightly at the poles due to rotation, with the equator bulging outward by about 21 kilometres compared to the poles. Both answers are approximations. The true shape of the Earth, defined by the actual distribution of mass and the resulting gravitational field, is much more irregular. The reference surface that captures this true shape is called the geoid, and it is one of the more subtle but important concepts in modern geography. The geoid is what an idealised global sea — calm, at rest, with no waves or tides — would settle into under the influence of gravity. It is the surface to which "mean sea level" notionally refers, the surface that bubble levels and plumb bobs respond to, and the surface from which true elevations should be measured.
The Reference Surface Problem
Maps and surveying require a reference surface — a defined shape against which heights, depths, and positions can be measured. The simplest reference is a sphere, but the Earth is detectably non-spherical. The next-best approximation is an ellipsoid — specifically the "Earth ellipsoid" or "reference ellipsoid," a mathematically defined shape that approximates the Earth's overall figure. The current standard reference ellipsoid is WGS 84 (World Geodetic System 1984), with an equatorial radius of 6,378,137 metres and a polar flattening of 1/298.257223563. GPS coordinates and most modern maps use WGS 84. But the actual Earth is not an ellipsoid. Density variations in the crust, mantle, and core create irregularities in the gravitational field, which in turn create irregularities in the natural reference surface for elevations — the geoid. Comparing the geoid to the reference ellipsoid, the differences (called "geoid undulations") range from about +85 metres to about -106 metres at different locations on the Earth's surface.
An Equipotential Surface
The geoid is formally defined as a particular equipotential surface of the Earth's gravitational field. An equipotential surface is one where the gravitational potential is constant — a marble placed anywhere on the surface would not roll, because there is no gravitational gradient along the surface to move it. Many such surfaces exist around the Earth, one at every potential value. The geoid is specifically the equipotential surface that most closely matches the average level of the world's oceans. Sea level itself is approximately a geoidal surface — water at rest under gravity settles into an equipotential configuration — though actual sea level deviates from the geoid by up to a metre due to currents, winds, temperature variations, salinity differences, and so on. The geoid is the idealised, gravity-only equilibrium sea surface.
Why Earth's Gravity Field Is Irregular
The Earth's gravity field would be uniform — varying only smoothly with latitude due to the equatorial bulge — if the planet were perfectly uniform in density at every depth. But the planet is not uniform. The continents (low-density continental crust) sit higher than ocean basins (denser oceanic crust beneath water). The mantle has lateral density variations associated with mantle convection and the legacy of past tectonics. The deep core-mantle boundary has temperature and chemical variations. Even the relatively thin layer of ocean water and atmosphere produces gravitational effects. All these density variations combine to produce the irregular pattern of geoid undulations observed today.
Major Features of the Geoid
The geoid map shows striking patterns when displayed. The lowest geoid (deepest "trough" relative to the ellipsoid) is in the Indian Ocean south of India, where the geoid is about 100 metres below the reference ellipsoid. This "Indian Ocean Geoid Low" has been intensively studied — it may be related to a deep mantle feature, possibly the buoyant mantle column rising beneath Africa pulling material upward from beneath the Indian Ocean. The highest geoid (largest "hill" relative to the ellipsoid) is in the western Pacific near New Guinea, about 80 metres above the ellipsoid. Other notable features include geoid highs over Iceland, the Andes, and the Himalayas (associated with various tectonic and mantle features), and geoid lows over Hudson Bay (linked to the legacy of the Laurentide ice sheet), the Caspian Sea region, and west of the Maldives.
How the Geoid Is Measured
Measuring the geoid requires measuring the Earth's gravity field with high precision over the entire planet. Historically this was done with land-based gravimeters at thousands of locations, supplemented by shipboard and airborne gravity surveys. Modern measurements increasingly come from dedicated satellites. The CHAMP (CHAllenging Minisatellite Payload), GRACE (Gravity Recovery And Climate Experiment), and GOCE (Gravity field and steady-state Ocean Circulation Explorer) missions in the 2000s and 2010s revolutionised geoid measurement. GRACE consisted of two satellites flying in formation, measuring tiny variations in their separation as one or the other passed over regions of slightly stronger or weaker gravity. GOCE used a high-precision gradiometer to measure spatial variations in gravity directly. The combined satellite data, integrated with traditional land-based gravity measurements, has produced geoid models with accuracy at the centimetre level over much of the Earth.
Why It Matters: Elevations
The geoid matters practically because it is the natural reference for elevations. When you stand at the seashore, the water at your feet is approximately at geoid level. Survey benchmarks were traditionally tied to local sea level, which means they were essentially tied to the local geoid. Heights given as "metres above sea level" are heights above the geoid. GPS, on the other hand, gives heights above the WGS 84 reference ellipsoid. The two can differ by up to 100 metres at any given location. To convert a GPS-derived ellipsoidal height into a useful elevation (meaningful for things like water flow direction, building grades, and the meaning of "above sea level"), you have to subtract the local geoid undulation. This conversion is now built into most consumer GPS receivers, but it requires a geoid model — the more accurate the geoid model, the more accurate the elevation conversion.
The Geoid and Sea Level Rise
The geoid is not static. Ice sheet changes shift mass between the cryosphere and the oceans, which redistributes gravity and changes the geoid. The melting of Greenland's ice sheet, for example, reduces the gravitational pull near Greenland (less ice mass), which causes sea level near Greenland to actually fall as water is "released" to flow elsewhere — the gravitational pull of the ice sheet was previously raising sea level near Greenland above the global average. Far from Greenland, the released water raises sea level. The "fingerprint" of sea level change from ice sheet melt is therefore not uniform — places far from the melting ice see more sea level rise than the global average, while places near the melting ice see less or even some sea level fall. The GRACE-FO satellite mission is currently providing ongoing measurements of these effects.
Geoid Anomalies and Geophysics
Geoid anomalies are direct windows into the interior of the Earth. A region with a positive geoid anomaly has, somewhere beneath it, more mass than the surrounding regions — typically dense, cold rock (subducted slabs, for instance) or sometimes mantle plumes. A negative anomaly indicates relatively low-mass material in the same region — typically hot rising plumes (which are buoyant) or thick continental crust roots. Some of the most distinctive geoid anomalies have helped geophysicists map deep mantle structure that would otherwise be invisible. The Indian Ocean Geoid Low, for example, is one of the largest persistent gravity features on the planet and has been used to test models of mantle dynamics for decades. The deep dipole of high geoid in the Western Pacific and low geoid in the Indian Ocean reflects the long-term effect of subduction in the Pacific and rising flow beneath Africa.
The Geoid in Daily Life
Most people will never need to think about the geoid, but its effects are everywhere. The water in your bathroom levels itself with the geoid (subject to building tilts and other local effects). The bubble in a carpenter's level responds to the geoid. The direction "down" — what a plumb bob hangs along — points along the local gravity vector, which is perpendicular to the geoid. Modern surveying, civil engineering, and infrastructure construction all rely on geoidal references. Aircraft altimeters typically reference local barometric pressure rather than the geoid directly, but the corrections involved are based on the geoidal definition of mean sea level. The geoid is, in a sense, the actual shape of the Earth as far as gravity is concerned — and gravity, more than anything else, defines what is up and down in our daily experience.